# Circles

A circle is a collection of points that are equidistant from the center point.

It is not a polygon because it does not have three or more sides!

Let’s breakdown that definition:

“Collection of points” means that a circle is made up a string of tiny points all touching each other so close that they look like a solid line.

“Equidistant” means that those points are all the same distance from the center of the circle. This means that the circle won’t have any lumps or bumps in it.

A circle has two main parts:

1. Radius: distance from the center to any point on the circle
2. Diameter: distance across the circle, going through the center (equal to two radii)

We can find the area and perimeter of a circle by using formulas. One difference for circles compared to other shapes is that instead of saying perimeter, we call the distance around the outside the circumference.

Area of a circle = πr

Circumference of a circle = 2πr

The symbol π stands for pi, which is a ratio of the circumference to the diameter of a circle. It is a non-terminating (never ending), non-repeating decimal that is often rounded to 3.14. Every time you see π in a formula, use 3.14 to solve the problem.

You can also do 1/4 or 1/2 circles, using your formula for area of a circle.

Just start with the formula above an divide it by 4 or 2 accordingly.

Example math problems related to circles:

1. Find the area and circumference of a circle with a radius of 3.5 cm.
• Start with the formula for area: πr2
• All we need to know is r = 3.5 and that π = 3.14 to use the formula:
• A = (3.14) x (3.5)2 = 38.465 sq. cm
• Circumference = 2πr
• C = 2 x (3.14) x (3.5) = 21.98 cm
2. Find the area and circumference of a circle with a diameter of 4 feet.
• Notice how this problem tells us diameter, but our formulas ask for radius. To find radius, we just need to divide the diameter by 2. So, 4 ÷ 2 = 2 ft. radius.
• Use the formulas as before:
• A = πr2 = (3.14) x (2)2 = 12.56 sq. cm
• C = 2πr = 2 x (3.14) x 2 = 12.56 cm
• A = 12.56 sq. cm, C = 12.56 cm)
3. How much will it cost to put a fence around a circular garden that has a radius of 5.2 ft. if the fence costs \$4.50 per foot?
• To start this problem first consider if you are going to find area or circumference. Since the fence will go around the garden, we will use the circumference formula since circumference describes the distance around the outside of a figure.
• C = 2πr = 2 x (3.14) x (5.2) = 32.656 ft.
• As always, make sure that when doing a word problem you answer the question. In this case we need to find the price of the fence. To do that, we multiply the circumference times the price per foot.
• 32.656 x 4.50 = \$146.95